Run additional code after user has executed and finished an operator
No, at least operators don't have the notion of a final state.

I can see in some cases you may want to setup a tools options, then perform some action once the options are set.

You could use a pop-up dialog 1 (as image-new does), but then you dont get feedback when changing values.

Some script writers add toggles to their operators that perform some extra calculation, so the user can choose to quickly setup options then press this last, while this isn't in keeping with our intended workflow, it makes some sense if the operator can't give interactive feedback because they're so slow.

There is one way you might be able to do what you want, and that is to create a Modal Operator, see the example in the text editor templates.
This way you start a tool which has its own mode (like grab or rotate), you can choose to handle events to adjust the settings, then a key such as Enter can finalize the operation.
So this may work in some cases - but modal operators assume a fairly different workflow so it depends a lot on what you do.